Adebayor was among the scorers as big-spending City made a compelling case for their ability to break the stranglehold of the "big four" in England, securing their fourth win out of four.
But he later made apologies over two controversial incidents that marked the game.
Champions Manchester United recovered from conceding an early goal at Tottenham Hotspur to win 3-1 even though Paul Scholes was sent off after an hour.
Chelsea maintained their perfect record with their fifth win but needed a last-minute Florent Malouda goal for a 2-1 victory at Stoke City.
Yossi Benayoun scored a hat-trick as Liverpool ended their sticky run by thrashing Burnley 4-0 at Anfield.
The results take Chelsea to 15 points with Manchester United, Manchester City and Spurs all on 12.
EASTLANDS DRAMA
City went ahead at Eastlands with an own goal via the head of Arsenal keeper Manuel Almunia, with the visitors levelling through Robin van Persie after 62 minutes.
City then cut loose with three goals in 10 minutes.
They regained the lead after 74 minutes through Craig Bellamy.
Adebayor, City's 25 million pounds summer signing from Arsenal, headed the third and Shaun Wright-Phillips then finished off a great breakaway.
Adebayor's decision to run the length of the pitch to celebrate his goal in front of the Arsenal fans earned him a booking but the Togo international, who has now scored in all four of City's league games, was quick to apologise.
"I shouldn't have done what I did but the emotion took over me and I'm sorry for what I've done," he told Sky Sports.
After the match had finished, Van Persie issued a statement via the club's official website accusing Adebayor of maliciously stamping on him. The City striker firmly denied that suggestion but expressed sorrow, saying he was trying to kick the ball, not his opponent's head.
"I did not have time to take back my feet," he said. "Because I was trying to kick the ball my feet touched his head. At the end of the game I told him I'm very sorry."
Czech midfielder Tomas Rosicky got Arsenal's late second.
Spurs, who had not beaten United in their last 19 meetings, went ahead inside a minute when in-form Jermain Defoe swept in a bicycle kick from a Peter Crouch knock-down.
Any thoughts of another upset win soon disappeared, though, as Ryan Giggs equalised with a free kick and Anderson's first goal for the club had the visitors deservedly ahead at half-time.
United had midfielder Scholes sent off for a second booking after an hour but remained the more dangerous side and wrapped up a terrific win with a length-of-the field counter-attack superbly finished by Wayne Rooney 13 minutes from time.
United play City next weekend.
Last season Chelsea scored twice in the last three minutes to claim a 2-1 comeback win over Stoke at Stamfor
